
#import sys
#!{sys.executable} -m pip install pandas-profiling

#Libraries to help with reading data and manipulating data
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Libraries that support data visualization
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns

# Libraries to suppress warnings
import warnings 
warnings.filterwarnings("ignore")

sns.set()

# to split the data into train and test
from sklearn.model_selection import train_test_split

# to build linear regression_model
from sklearn.linear_model import LinearRegression

# to check model performance
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score

# to build linear regression_model using statsmodels
import statsmodels.api as sm


#Load the dataset


data = pd.read_csv("used_phone_data.csv")


#copying data to another data frame to avaoid changes in the original data
df = data.copy()


df.head() # display 5 rows from the dataframe


df.shape

(3571, 15)


df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3571 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   brand_name        3571 non-null   object 
 1   os                3571 non-null   object 
 2   screen_size       3571 non-null   float64
 3   4g                3571 non-null   object 
 4   5g                3571 non-null   object 
 5   main_camera_mp    3391 non-null   float64
 6   selfie_camera_mp  3569 non-null   float64
 7   int_memory        3561 non-null   float64
 8   ram               3561 non-null   float64
 9   battery           3565 non-null   float64
 10  weight            3564 non-null   float64
 11  release_year      3571 non-null   int64  
 12  days_used         3571 non-null   int64  
 13  new_price         3571 non-null   float64
 14  used_price        3571 non-null   float64
dtypes: float64(9), int64(2), object(4)
memory usage: 418.6+ KB


df.describe().T


df.describe(exclude='number').T


category = ['brand_name', 'os', '4g', '5g']

for column in category:
    print(df[column].value_counts())
    print('_'*40)

Others        509
Samsung       364
Huawei        264
LG            212
Lenovo        172
ZTE           141
Xiaomi        134
Oppo          129
Asus          126
Alcatel       125
Nokia         121
Micromax      120
Honor         118
Vivo          117
HTC           110
Motorola      110
Sony           88
Meizu          62
Apple          59
Gionee         56
Acer           51
XOLO           49
Panasonic      47
Realme         41
Celkon         37
Lava           36
Karbonn        30
Spice          30
OnePlus        22
BlackBerry     22
Coolpad        22
Microsoft      22
Google         15
Infinix        10
Name: brand_name, dtype: int64
________________________________________
Android    3246
Others      202
Windows      67
iOS          56
Name: os, dtype: int64
________________________________________
yes    2359
no     1212
Name: 4g, dtype: int64
________________________________________
no     3419
yes     152
Name: 5g, dtype: int64
________________________________________


df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3571 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   brand_name        3571 non-null   object 
 1   os                3571 non-null   object 
 2   screen_size       3571 non-null   float64
 3   4g                3571 non-null   object 
 4   5g                3571 non-null   object 
 5   main_camera_mp    3391 non-null   float64
 6   selfie_camera_mp  3569 non-null   float64
 7   int_memory        3561 non-null   float64
 8   ram               3561 non-null   float64
 9   battery           3565 non-null   float64
 10  weight            3564 non-null   float64
 11  release_year      3571 non-null   int64  
 12  days_used         3571 non-null   int64  
 13  new_price         3571 non-null   float64
 14  used_price        3571 non-null   float64
dtypes: float64(9), int64(2), object(4)
memory usage: 418.6+ KB


print(df.brand_name.unique())

['Honor' 'Others' 'HTC' 'Huawei' 'Infinix' 'Lava' 'Lenovo' 'LG' 'Meizu'
 'Micromax' 'Motorola' 'Nokia' 'OnePlus' 'Oppo' 'Realme' 'Samsung' 'Vivo'
 'Xiaomi' 'ZTE' 'Apple' 'Asus' 'Coolpad' 'Acer' 'Alcatel' 'BlackBerry'
 'Celkon' 'Gionee' 'Google' 'Karbonn' 'Microsoft' 'Panasonic' 'Sony'
 'Spice' 'XOLO']


print(df.os.unique())

['Android' 'Others' 'iOS' 'Windows']


print(df['4g'].unique())

['yes' 'no']


print(df['5g'].unique())

['no' 'yes']


df.describe(include='all').T


 df.isna().sum()

brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
main_camera_mp      180
selfie_camera_mp      2
int_memory           10
ram                  10
battery               6
weight                7
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64


df.isnull().sum()

brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
main_camera_mp      180
selfie_camera_mp      2
int_memory           10
ram                  10
battery               6
weight                7
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64


df['os'] = df['os'].astype('category')


df['brand_name'] = df['brand_name'].astype('category')


df['5g'] = df['5g'].astype('category')


df['4g'] = df['4g'].astype('category')


sns.histplot(df.screen_size, kde=True);


sns.boxplot(df.screen_size,orient = "h");


sns.histplot(df.main_camera_mp, kde=True);


sns.boxplot(df.main_camera_mp,orient = "h");


sns.histplot(df.selfie_camera_mp, kde=True);


sns.histplot(df.int_memory, kde=True,binwidth=50);


sns.boxplot(df.int_memory,orient = "h");


sns.histplot(df.ram, kde=True);


sns.boxplot(df.ram,orient = "h");


sns.histplot(df.battery, kde=True);


sns.boxplot(df.battery,orient = "h");


sns.histplot(df.weight, kde=True, binwidth=50);


sns.boxplot(df.weight,orient = "h");


sns.histplot(df.release_year, kde=True);


sns.boxplot(df.release_year,orient = "h");


sns.histplot(df.days_used, kde=True);


sns.boxplot(df.days_used,orient = "h");


sns.histplot(df.new_price, kde=True, binwidth=50);


sns.boxplot(df.new_price,orient = "h");


sns.histplot(df.used_price, kde=True, binwidth=50);


sns.boxplot(df.used_price,orient = "h");


sns.histplot(df.os);


sns.histplot(df['4g']);


sns.histplot(df['5g']);


sns.heatmap(df.corr(),cmap="YlGnBu",vmin=-1,vmax=1, annot=True)

<AxesSubplot:>


sns.pairplot(df, hue='os');


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='release_year', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='days_used', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='new_price', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='ram', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='int_memory', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='weight', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='battery', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='main_camera_mp', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='selfie_camera_mp', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='screen_size', y = df['used_price'], data = df)


sns.countplot(x="os", hue="brand_name", data=df, palette='Set1',saturation=50 );


sns.countplot(x="os", hue="4g", data=df, palette='Set1',saturation=50 );


sns.countplot(x="os", hue="5g", data=df, palette='Set1',saturation=50 );


sns.countplot(x="5g", hue="brand_name", data=df, palette='Set1',saturation=50 );


sns.countplot(x="5g", hue="4g", data=df, palette='Set1',saturation=50 );


plt.figure(figsize=(15,5))

ax = sns.barplot(x='os', y='used_price', data=data)


plt.figure(figsize=(15,5))

ax = sns.barplot(x='brand_name', y='used_price', data=data)


plt.figure(figsize=(15,5))

ax = sns.barplot(x='4g', y='used_price', data=data)


plt.figure(figsize=(15,5))

ax = sns.barplot(x='5g', y='used_price', data=data)


#figure = plt.figure(figsize=(8,7))
#sns.barplot(x="brand_name", y="used_price", data=df, hue='os', palette='tab10' )
#plt.show()

g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "os", "used_price", order=["Android", "Others", "iOS", "Windows"])

<seaborn.axisgrid.FacetGrid at 0x1ff50840310>


g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "4g", "used_price", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff4b970d30>


g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "5g", "used_price", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff489b1f70>


g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "4g", "ram", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff50affc10>


g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "5g", "ram", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff580f0af0>


g = sns.FacetGrid(df, col="brand_name", height=4, aspect=.5)
g.map(sns.barplot, "os", "ram", order=["Android", "Others", "iOS", "Windows"])

<seaborn.axisgrid.FacetGrid at 0x1ff4bbe0d00>


sns.histplot(df.used_price, kde=True, binwidth=50);


sns.histplot(df.os);


def labeled_barplot(data, feature, perc=False, n=None):

    total = len(data[feature])  # length of the column
    count = data[feature].nunique()
    if n is None:
        plt.figure(figsize=(count + 1, 5))
    else:
        plt.figure(figsize=(n + 1, 5))

    plt.xticks(rotation=90, fontsize=15)
    ax = sns.countplot(
        data=data,
        x=feature,
        palette="Paired",
        order=data[feature].value_counts().index[:n].sort_values(),
    )

    for p in ax.patches:
        if perc == True:
            label = "{:.1f}%".format(
                100 * p.get_height() / total
            ) 
        else:
            label = p.get_height()  # count of each level of the category

        x = p.get_x() + p.get_width() / 2  # width of the plot
        y = p.get_height()  # height of the plot

        ax.annotate(
            label,
            (x, y),
            ha="center",
            va="center",
            size=12,
            xytext=(0, 5),
            textcoords="offset points",
        )  

    plt.show()


labeled_barplot(df, "os", perc=True)


g = sns.FacetGrid(df, col="brand_name")
g.map(sns.histplot, "ram")

#plt.figure(figsize=(20,5))

#ax = sns.jointplot(x='brand_name', y='ram', data=data)

<seaborn.axisgrid.FacetGrid at 0x1ff59291310>


df["heavybat"] = np.where(df["battery"] > 4500, "heavybat", "lightbat")


#fig = plt.figure(figsize= (10,5))
#ax = sns.regplot(x ='heavybat', y = df['weight'], data = df)
df


plt.figure(figsize=(15,5))

ax = sns.barplot(x=df['heavybat'], y='weight', data=data)


df["screen_grp"] = np.where(df["screen_size"] > 6, "larger_screen", "smaller_screen")


df["screen_grp"].value_counts()

larger_screen     3450
smaller_screen     121
Name: screen_grp, dtype: int64


sns.histplot(df.screen_grp);


temp = df[df['selfie_camera_mp'] > 8].copy()
temp


sns.histplot(temp.selfie_camera_mp);


sns.heatmap(df.corr(),cmap="YlGnBu",vmin=-1,vmax=1, annot=True)

<AxesSubplot:>


df = df.drop(['heavybat','screen_grp'],axis =1)


np.random.seed(42)


df.sample(n=10)#Return a random sample of 10 rows from the dataframe 'data'


df.isnull().sum().sort_values(ascending = False) 
#Return the count of missing values column-wise and sort them in descending order

main_camera_mp      180
int_memory           10
ram                  10
weight                7
battery               6
selfie_camera_mp      2
brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64


df.dropna(subset = ['used_price'], inplace = True)

df


medianFiller = lambda x: x.fillna(x.median())
numeric_columns = df.select_dtypes(include = np.number).columns.tolist()
df[numeric_columns] = df[numeric_columns].apply(medianFiller, axis = 0)


df.isnull().sum()

brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
dtype: int64


# Lets look at the statistical summary of the data
df.describe(include="all").T


# function to plot a boxplot and a histogram along the same scale.


def histogram_boxplot(data, feature, figsize=(12, 7), kde=False, bins=None):
    """
    Boxplot and histogram combined

    data: dataframe
    feature: dataframe column
    figsize: size of figure (default (12,7))
    kde: whether to the show density curve (default False)
    bins: number of bins for histogram (default None)
    """
    f2, (ax_box2, ax_hist2) = plt.subplots(
        nrows=2,  # Number of rows of the subplot grid= 2
        sharex=True,  # x-axis will be shared among all subplots
        gridspec_kw={"height_ratios": (0.25, 0.75)},
        figsize=figsize,
    )  # creating the 2 subplots
    sns.boxplot(
        data=data, x=feature, ax=ax_box2, showmeans=True, color="violet"
    )  # boxplot will be created and a star will indicate the mean value of the column
    sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
    ) if bins else sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2
    )  # For histogram
    ax_hist2.axvline(
        data[feature].mean(), color="green", linestyle="--"
    )  # Add mean to the histogram
    ax_hist2.axvline(
        data[feature].median(), color="black", linestyle="-"
    )  # Add median to the histogram


histogram_boxplot(df,"used_price")


df['brand_type'] = pd.cut(data['new_price'], bins = [0,500,1500,3000], labels = ['Low', 'Medium', 'High'])

df


df['brand_type'].value_counts()

Low       3325
Medium     237
High         9
Name: brand_type, dtype: int64


df['brand_type'].unique()

['Low', 'Medium', 'High']
Categories (3, object): ['Low' < 'Medium' < 'High']


df.isnull().sum() # checking for null-values

brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
brand_type          0
dtype: int64


sns.histplot(df["brand_type"])

<AxesSubplot:xlabel='brand_type', ylabel='Count'>


 #let's plot the boxplots of all columns to check for outliers
plt.figure(figsize=(20, 30))

for i, variable in enumerate(numeric_columns):
    plt.subplot(5, 4, i + 1)
    plt.boxplot(df[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()


# Outlier treatment
def treatment_outliers(df, col):
    
    Q1 = df[col].quantile(0.25)  # 25th quantile
    Q3 = df[col].quantile(0.75)  # 75th quantile
    IQR = Q3 - Q1
    Lower_Whisker = Q1 - 1.5 * IQR
    Upper_Whisker = Q3 + 1.5 * IQR

    # all the values smaller than Lower_Whisker will be assigned the value of Lower_Whisker
    # all the values greater than Upper_Whisker will be assigned the value of Upper_Whisker
    df[col] = np.clip(df[col], Lower_Whisker, Upper_Whisker)

    return df


def treat_all_outliers(df, col_list):
    for c in col_list:
        df = treatment_outliers(df, c)

    return df


# treating the outliers
numerical_col = df.select_dtypes(include=np.number).columns.tolist()
df = treat_all_outliers(df, numerical_col)


# let's look at the boxplots to see if the outliers have been treated or not
plt.figure(figsize=(20, 30))

for i, variable in enumerate(numeric_columns):
    plt.subplot(5, 4, i + 1)
    plt.boxplot(df[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()


df.head()


df.shape

(3571, 16)


df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3571 entries, 0 to 3570
Data columns (total 16 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3571 non-null   category
 1   os                3571 non-null   category
 2   screen_size       3571 non-null   float64 
 3   4g                3571 non-null   category
 4   5g                3571 non-null   category
 5   main_camera_mp    3571 non-null   float64 
 6   selfie_camera_mp  3571 non-null   float64 
 7   int_memory        3571 non-null   float64 
 8   ram               3571 non-null   float64 
 9   battery           3571 non-null   float64 
 10  weight            3571 non-null   float64 
 11  release_year      3571 non-null   int64   
 12  days_used         3571 non-null   int64   
 13  new_price         3571 non-null   float64 
 14  used_price        3571 non-null   float64 
 15  brand_type        3571 non-null   category
dtypes: category(5), float64(9), int64(2)
memory usage: 354.1 KB


df.describe().T


df.describe(exclude='number').T


category = ['brand_name', 'os', '4g', '5g','brand_type']

for column in category:
    print(df[column].value_counts())
    print('_'*40)

Others        509
Samsung       364
Huawei        264
LG            212
Lenovo        172
ZTE           141
Xiaomi        134
Oppo          129
Asus          126
Alcatel       125
Nokia         121
Micromax      120
Honor         118
Vivo          117
HTC           110
Motorola      110
Sony           88
Meizu          62
Apple          59
Gionee         56
Acer           51
XOLO           49
Panasonic      47
Realme         41
Celkon         37
Lava           36
Karbonn        30
Spice          30
Microsoft      22
OnePlus        22
Coolpad        22
BlackBerry     22
Google         15
Infinix        10
Name: brand_name, dtype: int64
________________________________________
Android    3246
Others      202
Windows      67
iOS          56
Name: os, dtype: int64
________________________________________
yes    2359
no     1212
Name: 4g, dtype: int64
________________________________________
no     3419
yes     152
Name: 5g, dtype: int64
________________________________________
Low       3325
Medium     237
High         9
Name: brand_type, dtype: int64
________________________________________


df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3571 entries, 0 to 3570
Data columns (total 16 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3571 non-null   category
 1   os                3571 non-null   category
 2   screen_size       3571 non-null   float64 
 3   4g                3571 non-null   category
 4   5g                3571 non-null   category
 5   main_camera_mp    3571 non-null   float64 
 6   selfie_camera_mp  3571 non-null   float64 
 7   int_memory        3571 non-null   float64 
 8   ram               3571 non-null   float64 
 9   battery           3571 non-null   float64 
 10  weight            3571 non-null   float64 
 11  release_year      3571 non-null   int64   
 12  days_used         3571 non-null   int64   
 13  new_price         3571 non-null   float64 
 14  used_price        3571 non-null   float64 
 15  brand_type        3571 non-null   category
dtypes: category(5), float64(9), int64(2)
memory usage: 354.1 KB


print(df.brand_name.unique())

['Honor', 'Others', 'HTC', 'Huawei', 'Infinix', ..., 'Microsoft', 'Panasonic', 'Sony', 'Spice', 'XOLO']
Length: 34
Categories (34, object): ['Honor', 'Others', 'HTC', 'Huawei', ..., 'Panasonic', 'Sony', 'Spice', 'XOLO']


print(df.os.unique())

['Android', 'Others', 'iOS', 'Windows']
Categories (4, object): ['Android', 'Others', 'iOS', 'Windows']


print(df['4g'].unique())

['yes', 'no']
Categories (2, object): ['yes', 'no']


print(df['5g'].unique())

['no', 'yes']
Categories (2, object): ['no', 'yes']


print(df['brand_type'].unique())

['Low', 'Medium', 'High']
Categories (3, object): ['Low' < 'Medium' < 'High']


df.describe(include='all').T


df.isna().sum()

brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
brand_type          0
dtype: int64


df.isnull().sum()

brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
brand_type          0
dtype: int64


df['os'] = df['os'].astype('category')


df['brand_name'] = df['brand_name'].astype('category')


df['5g'] = df['5g'].astype('category')


df['4g'] = df['4g'].astype('category')


df['brand_type'] = df['brand_type'].astype('category')


sns.histplot(df.screen_size, kde=True);


sns.boxplot(df.screen_size,orient = "h");


sns.histplot(df.main_camera_mp, kde=True);


sns.boxplot(df.main_camera_mp,orient = "h");


sns.histplot(df.selfie_camera_mp, kde=True);


sns.histplot(df.int_memory, kde=True,binwidth=50);


sns.histplot(df.ram, kde=True);


sns.histplot(df.battery, kde=True);


sns.histplot(df.weight, kde=True, binwidth=50);


sns.histplot(df.release_year, kde=True);


sns.histplot(df.days_used, kde=True);


sns.histplot(df.new_price, kde=True, binwidth=50);


sns.histplot(df.used_price, kde=True, binwidth=50);


sns.histplot(df.os);


sns.histplot(df['4g']);


sns.histplot(df['5g']);


sns.histplot(df.brand_type);


sns.heatmap(df.corr(),cmap="YlGnBu",vmin=-1,vmax=1, annot=True)

<AxesSubplot:>


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='release_year', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='days_used', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='new_price', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='ram', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='int_memory', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='weight', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='battery', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='main_camera_mp', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='selfie_camera_mp', y = df['used_price'], data = df)


fig = plt.figure(figsize= (10,5))
ax = sns.regplot(x ='screen_size', y = df['used_price'], data = df)


sns.countplot(x="os", hue="brand_type", data=df, palette='Set1',saturation=50 );


sns.countplot(x="os", hue="5g", data=df, palette='Set1',saturation=50 );


sns.countplot(x="5g", hue="brand_type", data=df, palette='Set1',saturation=50 );


sns.countplot(x="5g", hue="4g", data=df, palette='Set1',saturation=50 );


plt.figure(figsize=(15,5))

ax = sns.barplot(x='os', y='used_price', data=data)


plt.figure(figsize=(15,5))

ax = sns.barplot(x='4g', y='used_price', data=data)


plt.figure(figsize=(15,5))

ax = sns.barplot(x='5g', y='used_price', data=data)


#figure = plt.figure(figsize=(8,7))
#sns.barplot(x="brand_name", y="used_price", data=df, hue='os', palette='tab10' )
#plt.show()

g = sns.FacetGrid(df, col="brand_type", height=4, aspect=.5)
g.map(sns.barplot, "os", "used_price", order=["Android", "Others", "iOS", "Windows"])

<seaborn.axisgrid.FacetGrid at 0x1ff6682aeb0>


g = sns.FacetGrid(df, col="brand_type", height=4, aspect=.5)
g.map(sns.barplot, "4g", "used_price", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff66a43d00>


g = sns.FacetGrid(df, col="brand_type", height=4, aspect=.5)
g.map(sns.barplot, "5g", "used_price", order=["yes", "no"])

<seaborn.axisgrid.FacetGrid at 0x1ff66b32610>


sns.histplot(df.used_price, kde=True, binwidth=50);


sns.histplot(df.os);


labeled_barplot(df, "os", perc=True)


g = sns.FacetGrid(df, col="brand_name")
g.map(sns.histplot, "ram")

<seaborn.axisgrid.FacetGrid at 0x1ff66372790>


df["heavybat"] = np.where(df["battery"] > 4500, "heavybat", "lightbat")


plt.figure(figsize=(15,5))

ax = sns.barplot(x=df['heavybat'], y='weight', data=data)


df["screen_grp"] = np.where(df["screen_size"] > 6, "larger_screen", "smaller_screen")


df["screen_grp"].value_counts()

larger_screen    3571
Name: screen_grp, dtype: int64


sns.histplot(df.screen_grp);


temp = df[df['selfie_camera_mp'] > 8].copy()
temp


sns.histplot(temp.selfie_camera_mp);


sns.heatmap(df.corr(),cmap="YlGnBu",vmin=-1,vmax=1, annot=True)

<AxesSubplot:>


df = df.drop(['heavybat','screen_grp'],axis =1)


# defining X and y variables.
# ram variable is highly skewed. For most of the phones it is 4GB. Hence, dropping the column
X = df.drop(['used_price','brand_name', 'ram'], axis = 1) #ram
y = df['used_price']


X.head()


y.head()

0     86.9600
1    161.4900
2    247.1925
3    180.2300
4    103.8000
Name: used_price, dtype: float64


X = pd.get_dummies(X, columns = X.select_dtypes(include = ["object","category"]).columns.tolist(), drop_first = True)


X.head()


y.head()

0     86.9600
1    161.4900
2    247.1925
3    180.2300
4    103.8000
Name: used_price, dtype: float64


# Splitting the data into test and train data

x_train, x_test, y_train, y_test = train_test_split(X,y, test_size = 0.3, random_state = 42)
x_train_ols = x_train.copy()
y_train_ols = y_train.copy()
x_test_ols = x_test.copy()
y_test_ols = y_test.copy()


x_train.shape[0]

2499


x_test.shape[0]

1072


# fit the model on the train data

from sklearn.linear_model import LinearRegression

linearregression = LinearRegression()
linearregression.fit(x_train, y_train)

LinearRegression()


coef_df = pd.DataFrame(np.append(linearregression.coef_, linearregression.intercept_), index = x_train.columns.tolist()+ ["Intercept"], columns = ["Coefficients"])
coef_df


# Adjusted r-square
def adj_r2(predictors, targets, predictions):
    r2 = r2_score(targets, predictions)
    n = predictors.shape[0]
    k = predictors.shape[1]
    return 1-((1-r2)*(n-1)/(n-k-1))

def mape_score(targets, predictions):
    return np.mean(np.abs(targets -predictions)/targets) * 100

def model_perf_regression(model, predictors, target):
    pred = model.predict(predictors)
    r2 = r2_score(target,pred)
    adjr2 = adj_r2(predictors, target, pred)
    rmse = np.sqrt(mean_squared_error(target,pred))
    mae = mean_absolute_error(target, pred)
    mape = mape_score(target,pred)
    
    # creating dataframe of metrics
    df_performance = pd.DataFrame({
        "RMSE": rmse,
        "MAE": mae,
        "R-Squared": r2,
        "Adj. R-Squared": adjr2,
        "MAPE": mape,
        }, 
        index=[0],
    )
    return df_performance


# check train set performance
print("Training set performance\n")
linearregression_train_performance = model_perf_regression(linearregression, x_train, y_train)
linearregression_train_performance

Training set performance


# check test set performance
print("Test Set Performance\n")
linearregression_test_performance = model_perf_regression(linearregression, x_test, y_test)
linearregression_test_performance

Test Set Performance


# Statsmodel doesnot add a constant to the data on its own. Here the constant needs to be added manually. 
x_train1 = sm.add_constant(x_train) # has_constant='add'
x_test1 = sm.add_constant(x_test)
olsmod0 = sm.OLS(y_train, x_train1).fit()
print(olsmod0.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:             used_price   R-squared:                       0.955
Model:                            OLS   Adj. R-squared:                  0.955
Method:                 Least Squares   F-statistic:                     3293.
Date:                Fri, 20 Aug 2021   Prob (F-statistic):               0.00
Time:                        22:01:53   Log-Likelihood:                -10137.
No. Observations:                2499   AIC:                         2.031e+04
Df Residuals:                    2482   BIC:                         2.041e+04
Df Model:                          16                                         
Covariance Type:            nonrobust                                         
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
const              -314.9593    540.308     -0.583      0.560   -1374.460     744.541
screen_size           0.0944      0.121      0.779      0.436      -0.143       0.332
main_camera_mp       -0.3094      0.087     -3.561      0.000      -0.480      -0.139
selfie_camera_mp      0.6163      0.100      6.165      0.000       0.420       0.812
int_memory            0.0949      0.010      9.445      0.000       0.075       0.115
battery              -0.0001      0.000     -0.305      0.760      -0.001       0.001
weight               -0.0052      0.012     -0.432      0.666      -0.029       0.018
release_year          0.1868      0.268      0.697      0.486      -0.339       0.712
days_used            -0.0854      0.002    -47.774      0.000      -0.089      -0.082
new_price             0.4056      0.004    106.127      0.000       0.398       0.413
os_Others            -4.7890      1.355     -3.533      0.000      -7.447      -2.131
os_Windows           -1.2333      2.066     -0.597      0.551      -5.285       2.819
os_iOS                8.6583      2.473      3.501      0.000       3.809      13.508
4g_yes               -3.7920      0.874     -4.338      0.000      -5.506      -2.078
5g_yes                2.7110      1.693      1.601      0.109      -0.609       6.030
brand_type_Medium   -14.3824      1.627     -8.842      0.000     -17.572     -11.193
brand_type_High     -26.3773      6.428     -4.104      0.000     -38.981     -13.773
==============================================================================
Omnibus:                      227.169   Durbin-Watson:                   1.978
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              491.543
Skew:                           0.569   Prob(JB):                    1.83e-107
Kurtosis:                       4.851   Cond. No.                     7.39e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.39e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


from statsmodels.stats.outliers_influence import variance_inflation_factor

def checking_vif(predictors):
    vif = pd.DataFrame()
    vif["feature"] = predictors.columns
    vif["VIF"] = [variance_inflation_factor(predictors.values,i)
                 for i in range(len(predictors.columns))
    ]
    return vif


checking_vif(x_train1)


# initial list of columns
cols = x_train1.columns.tolist()

# setting an initial max p-value
max_p_value = 1

while len(cols) > 0:
    # defining the train set
    x_train_aux = x_train1[cols]

    # fitting the model
    model = sm.OLS(y_train, x_train_aux).fit()

    # getting the p-values and the maximum p-value
    p_values = model.pvalues
    max_p_value = max(p_values)

    # name of the variable with maximum p-value
    feature_with_p_max = p_values.idxmax()

    if max_p_value > 0.05:
        cols.remove(feature_with_p_max)
    else:
        break

selected_features = cols
print(selected_features)

['main_camera_mp', 'selfie_camera_mp', 'int_memory', 'release_year', 'days_used', 'new_price', 'os_Others', 'os_iOS', '4g_yes', 'brand_type_Medium', 'brand_type_High']


x_train2 = x_train1[selected_features]
x_test2 = x_test1[selected_features]


olsmod2 = sm.OLS(y_train, x_train2).fit()
print(olsmod2.summary())

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:             used_price   R-squared (uncentered):                   0.985
Model:                            OLS   Adj. R-squared (uncentered):              0.985
Method:                 Least Squares   F-statistic:                          1.517e+04
Date:                Fri, 20 Aug 2021   Prob (F-statistic):                        0.00
Time:                        22:02:06   Log-Likelihood:                         -10140.
No. Observations:                2499   AIC:                                  2.030e+04
Df Residuals:                    2488   BIC:                                  2.037e+04
Df Model:                          11                                                  
Covariance Type:            nonrobust                                                  
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
main_camera_mp       -0.3342      0.083     -4.041      0.000      -0.496      -0.172
selfie_camera_mp      0.6697      0.088      7.621      0.000       0.497       0.842
int_memory            0.0974      0.010      9.781      0.000       0.078       0.117
release_year          0.0309      0.001     45.263      0.000       0.030       0.032
days_used            -0.0865      0.001    -59.610      0.000      -0.089      -0.084
new_price             0.4059      0.003    118.789      0.000       0.399       0.413
os_Others            -4.9837      1.253     -3.977      0.000      -7.441      -2.526
os_iOS                8.6099      2.421      3.557      0.000       3.863      13.356
4g_yes               -3.6670      0.792     -4.629      0.000      -5.220      -2.114
brand_type_Medium   -14.0870      1.580     -8.918      0.000     -17.185     -10.989
brand_type_High     -25.5026      6.387     -3.993      0.000     -38.027     -12.978
==============================================================================
Omnibus:                      230.585   Durbin-Watson:                   1.976
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              492.220
Skew:                           0.581   Prob(JB):                    1.31e-107
Kurtosis:                       4.838   Cond. No.                     4.87e+04
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 4.87e+04. This might indicate that there are
strong multicollinearity or other numerical problems.


#j=0
#for i in ('battery', 'weight', 'os_Windows', 'release_year'):
 #   print(i)
  #  x_train_j = sm.add_constant(x_train.drop(i,axis=1)) # has_constant='add'
   # x_test_j = sm.add_constant(x_test.drop(i,axis=1))
   # olsmod_j = sm.OLS(y_train, x_train_j).fit()
   # print(olsmod_j.summary())
    #j=j+1


# Statsmodel doesnot add a constant to the data on its own. Here the constant needs to be added manually. 
#olsmod1 = sm.OLS(y_train, x_train1.drop("release_year", axis=1)).fit()
#print(olsmod1.summary())


#checking_vif(x_train1.drop("release_year", axis=1))


# let us create a dataframe with aactual, fitted and residual values
df_pred = pd.DataFrame()

df_pred["Actual Values"] = y_train  # actual values
df_pred["Fitted Values"] = olsmod2.fittedvalues  # predicted values
df_pred["Residuals"] = olsmod2.resid  # residuals

df_pred.head()


# let's plot the fitted values vs residuals

sns.residplot(
    data=df_pred, x="Fitted Values", y="Residuals", color="purple", lowess=True
)
plt.xlabel("Fitted Values")
plt.ylabel("Residuals")
plt.title("Fitted vs Residual plot")
plt.show()


sns.histplot(data=df_pred, x="Residuals", kde=True)
plt.title("Normality of residuals")
plt.show()


import pylab
import scipy.stats as stats

stats.probplot(df_pred["Residuals"], dist="norm", plot=pylab)
plt.show()


stats.shapiro(df_pred["Residuals"])

ShapiroResult(statistic=0.9706025719642639, pvalue=3.120287435108585e-22)


import statsmodels.stats.api as sms
from statsmodels.compat import lzip

name = ["F statistic", "p-value"]
test = sms.het_goldfeldquandt(df_pred["Residuals"], x_train2)
lzip(name, test)

[('F statistic', 1.0468462382983947), ('p-value', 0.2102941600456584)]


# predictions on the test set
pred = olsmod2.predict(x_test2)

df_pred_test = pd.DataFrame({"Actual": y_test, "Predicted": pred})
df_pred_test.sample(10, random_state=1)


df1 = df_pred_test.sample(25, random_state=1)
df1.plot(kind="bar", figsize=(15, 7))
plt.show()


# checking model performance on train set (seen 70% data)
print("Training Performance\n")
olsmod2_train_perf = model_perf_regression(olsmod2, x_train2, y_train)
olsmod2_train_perf

Training Performance


# checking model performance on test set (seen 30% data)
print("Test Performance\n")
olsmod2_test_perf = model_perf_regression(olsmod0, x_test1, y_test)
olsmod2_test_perf

Test Performance


# training performance comparison

models_train_comp_df = pd.concat(
    [linearregression_train_performance.T, olsmod2_train_perf.T],
    axis=1,
)

models_train_comp_df.columns = [
    "Linear Regression sklearn",
    "Linear Regression statsmodels",
]

print("Training performance comparison:")
models_train_comp_df

Training performance comparison:


# test performance comparison

models_test_comp_df = pd.concat(
    [linearregression_test_performance.T, olsmod2_test_perf.T],
    axis=1,
)

models_test_comp_df.columns = [
    "Linear Regression sklearn",
    "Linear Regression statsmodels",
]

print("Test performance comparison:")
models_test_comp_df

Test performance comparison:


olsmodel_final = sm.OLS(y_train, x_train2).fit()
print(olsmodel_final.summary())

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:             used_price   R-squared (uncentered):                   0.985
Model:                            OLS   Adj. R-squared (uncentered):              0.985
Method:                 Least Squares   F-statistic:                          1.517e+04
Date:                Fri, 20 Aug 2021   Prob (F-statistic):                        0.00
Time:                        22:03:25   Log-Likelihood:                         -10140.
No. Observations:                2499   AIC:                                  2.030e+04
Df Residuals:                    2488   BIC:                                  2.037e+04
Df Model:                          11                                                  
Covariance Type:            nonrobust                                                  
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
main_camera_mp       -0.3342      0.083     -4.041      0.000      -0.496      -0.172
selfie_camera_mp      0.6697      0.088      7.621      0.000       0.497       0.842
int_memory            0.0974      0.010      9.781      0.000       0.078       0.117
release_year          0.0309      0.001     45.263      0.000       0.030       0.032
days_used            -0.0865      0.001    -59.610      0.000      -0.089      -0.084
new_price             0.4059      0.003    118.789      0.000       0.399       0.413
os_Others            -4.9837      1.253     -3.977      0.000      -7.441      -2.526
os_iOS                8.6099      2.421      3.557      0.000       3.863      13.356
4g_yes               -3.6670      0.792     -4.629      0.000      -5.220      -2.114
brand_type_Medium   -14.0870      1.580     -8.918      0.000     -17.185     -10.989
brand_type_High     -25.5026      6.387     -3.993      0.000     -38.027     -12.978
==============================================================================
Omnibus:                      230.585   Durbin-Watson:                   1.976
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              492.220
Skew:                           0.581   Prob(JB):                    1.31e-107
Kurtosis:                       4.838   Cond. No.                     4.87e+04
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 4.87e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

	count	mean	std	min	25%	50%	75%	max
screen_size	3571.0	14.803892	5.153092	2.700	12.700	13.49	16.510	46.36
main_camera_mp	3391.0	9.400454	4.818396	0.080	5.000	8.00	13.000	48.00
selfie_camera_mp	3569.0	6.547352	6.879359	0.300	2.000	5.00	8.000	32.00
int_memory	3561.0	54.532607	84.696246	0.005	16.000	32.00	64.000	1024.00
ram	3561.0	4.056962	1.391844	0.030	4.000	4.00	4.000	16.00
battery	3565.0	3067.225666	1364.206665	80.000	2100.000	3000.00	4000.000	12000.00
weight	3564.0	179.424285	90.280856	23.000	140.000	159.00	184.000	950.00
release_year	3571.0	2015.964996	2.291784	2013.000	2014.000	2016.00	2018.000	2020.00
days_used	3571.0	675.391487	248.640972	91.000	536.000	690.00	872.000	1094.00
new_price	3571.0	237.389037	197.545581	9.130	120.130	189.80	291.935	2560.20
used_price	3571.0	109.880277	121.501226	2.510	45.205	75.53	126.000	1916.54

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
brand_name	3571	34	Others	509	NaN	NaN	NaN	NaN	NaN	NaN	NaN
os	3571	4	Android	3246	NaN	NaN	NaN	NaN	NaN	NaN	NaN
screen_size	3571.0	NaN	NaN	NaN	14.803892	5.153092	2.7	12.7	13.49	16.51	46.36
4g	3571	2	yes	2359	NaN	NaN	NaN	NaN	NaN	NaN	NaN
5g	3571	2	no	3419	NaN	NaN	NaN	NaN	NaN	NaN	NaN
main_camera_mp	3391.0	NaN	NaN	NaN	9.400454	4.818396	0.08	5.0	8.0	13.0	48.0
selfie_camera_mp	3569.0	NaN	NaN	NaN	6.547352	6.879359	0.3	2.0	5.0	8.0	32.0
int_memory	3561.0	NaN	NaN	NaN	54.532607	84.696246	0.005	16.0	32.0	64.0	1024.0
ram	3561.0	NaN	NaN	NaN	4.056962	1.391844	0.03	4.0	4.0	4.0	16.0
battery	3565.0	NaN	NaN	NaN	3067.225666	1364.206665	80.0	2100.0	3000.0	4000.0	12000.0
weight	3564.0	NaN	NaN	NaN	179.424285	90.280856	23.0	140.0	159.0	184.0	950.0
release_year	3571.0	NaN	NaN	NaN	2015.964996	2.291784	2013.0	2014.0	2016.0	2018.0	2020.0
days_used	3571.0	NaN	NaN	NaN	675.391487	248.640972	91.0	536.0	690.0	872.0	1094.0
new_price	3571.0	NaN	NaN	NaN	237.389037	197.545581	9.13	120.13	189.8	291.935	2560.2
used_price	3571.0	NaN	NaN	NaN	109.880277	121.501226	2.51	45.205	75.53	126.0	1916.54

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
457	Acer	Android	10.95	yes	no	5.0	2.0	32.0	4.0	2000.0	145.0	2015	1044	129.00	38.77
1647	Lenovo	Android	25.56	yes	no	8.0	1.6	16.0	4.0	9600.0	619.0	2014	723	300.61	120.29
351	Oppo	Android	23.97	yes	yes	NaN	32.0	128.0	8.0	4000.0	172.0	2020	293	470.81	335.09
1667	Lenovo	Android	12.70	no	no	13.0	5.0	16.0	4.0	2000.0	140.0	2014	721	199.93	80.14
1849	LG	Android	10.64	no	no	8.0	0.3	16.0	4.0	2460.0	115.5	2013	644	150.71	60.18
2111	Nokia	Android	23.97	yes	no	5.0	8.0	32.0	4.0	3000.0	161.0	2019	492	149.04	74.56
1366	Huawei	Android	12.70	yes	no	13.0	5.0	16.0	4.0	2200.0	140.0	2016	1069	130.90	39.27
70	Lenovo	Android	20.32	yes	no	13.0	5.0	16.0	2.0	5100.0	305.0	2019	461	158.56	79.14
1206	HTC	Android	13.81	yes	no	13.0	13.0	64.0	4.0	3075.0	150.0	2018	687	200.26	80.33
1213	HTC	Android	13.02	yes	no	16.0	16.0	64.0	4.0	2600.0	142.0	2017	859	210.26	63.02

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
brand_name	3571	34	Others	509	NaN	NaN	NaN	NaN	NaN	NaN	NaN
os	3571	4	Android	3246	NaN	NaN	NaN	NaN	NaN	NaN	NaN
screen_size	3571.0	NaN	NaN	NaN	14.803892	5.153092	2.7	12.7	13.49	16.51	46.36
4g	3571	2	yes	2359	NaN	NaN	NaN	NaN	NaN	NaN	NaN
5g	3571	2	no	3419	NaN	NaN	NaN	NaN	NaN	NaN	NaN
main_camera_mp	3571.0	NaN	NaN	NaN	9.329863	4.705341	0.08	5.0	8.0	13.0	48.0
selfie_camera_mp	3571.0	NaN	NaN	NaN	6.546486	6.877529	0.3	2.0	5.0	8.0	32.0
int_memory	3571.0	NaN	NaN	NaN	54.469509	84.585924	0.005	16.0	32.0	64.0	1024.0
ram	3571.0	NaN	NaN	NaN	4.056802	1.389897	0.03	4.0	4.0	4.0	16.0
battery	3571.0	NaN	NaN	NaN	3067.112714	1363.062572	80.0	2100.0	3000.0	4000.0	12000.0
weight	3571.0	NaN	NaN	NaN	179.384248	90.196828	23.0	140.0	159.0	184.0	950.0
release_year	3571.0	NaN	NaN	NaN	2015.964996	2.291784	2013.0	2014.0	2016.0	2018.0	2020.0
days_used	3571.0	NaN	NaN	NaN	675.391487	248.640972	91.0	536.0	690.0	872.0	1094.0
new_price	3571.0	NaN	NaN	NaN	237.389037	197.545581	9.13	120.13	189.8	291.935	2560.2
used_price	3571.0	NaN	NaN	NaN	109.880277	121.501226	2.51	45.205	75.53	126.0	1916.54

	count	mean	std	min	25%	50%	75%	max
screen_size	3571.0	14.521803	4.165771	6.985	12.700	13.49	16.510	22.2250
main_camera_mp	3571.0	9.299619	4.530650	0.080	5.000	8.00	13.000	25.0000
selfie_camera_mp	3571.0	5.972417	5.287271	0.300	2.000	5.00	8.000	17.0000
int_memory	3571.0	44.583202	38.938853	0.005	16.000	32.00	64.000	136.0000
ram	3571.0	4.000000	0.000000	4.000	4.000	4.00	4.000	4.0000
battery	3571.0	3042.193083	1272.573404	80.000	2100.000	3000.00	4000.000	6850.0000
weight	3571.0	164.415584	41.098253	74.000	140.000	159.00	184.000	250.0000
release_year	3571.0	2015.964996	2.291784	2013.000	2014.000	2016.00	2018.000	2020.0000
days_used	3571.0	675.391487	248.640972	91.000	536.000	690.00	872.000	1094.0000
new_price	3571.0	221.841506	135.411699	9.130	120.130	189.80	291.935	549.6425
used_price	3571.0	95.528957	66.145611	2.510	45.205	75.53	126.000	247.1925

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
0	Honor	Android	23.97	yes	no	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.62	86.96
1	Honor	Android	28.10	yes	yes	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.39	161.49
2	Honor	Android	24.29	yes	yes	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.47	268.55
3	Honor	Android	26.04	yes	yes	13.0	8.0	64.0	6.0	7250.0	480.0	2020	345	278.93	180.23
4	Honor	Android	15.72	yes	no	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.87	103.80

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price	brand_type
0	Honor	Android	22.225	yes	no	13.0	5.0	64.0	4.0	3020.0	146.0	2020	127	111.62	86.9600	Low
1	Honor	Android	22.225	yes	yes	13.0	16.0	128.0	4.0	4300.0	213.0	2020	325	249.39	161.4900	Low
2	Honor	Android	22.225	yes	yes	13.0	8.0	128.0	4.0	4200.0	213.0	2020	162	359.47	247.1925	Low
3	Honor	Android	22.225	yes	yes	13.0	8.0	64.0	4.0	6850.0	250.0	2020	345	278.93	180.2300	Low
4	Honor	Android	15.720	yes	no	13.0	8.0	64.0	4.0	5000.0	185.0	2020	293	140.87	103.8000	Low

	Coefficients
screen_size	0.094370
main_camera_mp	-0.309414
selfie_camera_mp	0.616280
int_memory	0.094922
battery	-0.000129
weight	-0.005222
release_year	0.186794
days_used	-0.085353
new_price	0.405613
os_Others	-4.789019
os_Windows	-1.233302
os_iOS	8.658309
4g_yes	-3.792003
5g_yes	2.710973
brand_type_Medium	-14.382445
brand_type_High	-26.377297
Intercept	-314.959332

	feature	VIF
0	const	3.707300e+06
1	screen_size	3.231782e+00
2	main_camera_mp	2.009739e+00
3	selfie_camera_mp	3.556360e+00
4	int_memory	1.934750e+00
5	battery	3.597409e+00
6	weight	3.070146e+00
7	release_year	4.818425e+00
8	days_used	2.548222e+00
9	new_price	3.377643e+00
10	os_Others	1.332737e+00
11	os_Windows	1.021507e+00
12	os_iOS	1.132857e+00
13	4g_yes	2.194265e+00
14	5g_yes	1.438091e+00
15	brand_type_Medium	2.025408e+00
16	brand_type_High	1.047651e+00

	Actual Values	Fitted Values	Residuals
844	100.48	102.074477	-1.594477
1539	111.68	118.123664	-6.443664
3452	113.89	110.904820	2.985180
1727	64.09	69.434766	-5.344766
1926	67.95	68.864293	-0.914293

	Actual	Predicted
2098	30.5200	21.695159
278	195.6700	192.070230
26	247.1925	229.477471
2910	89.9700	91.721518
2631	69.2000	64.044985
1582	89.5800	109.812760
2110	247.1925	264.449155
3160	65.3400	65.208595
2817	115.7700	106.862134
549	39.2900	47.590057

	Linear Regression sklearn	Linear Regression statsmodels
RMSE	13.980191	13.992121
MAE	10.344831	10.363142
R-Squared	0.955009	0.954932
Adj. R-Squared	0.954718	0.954732
MAPE	19.115553	19.248020

	Linear Regression sklearn	Linear Regression statsmodels
RMSE	13.617565	13.617565
MAE	10.161106	10.161106
R-Squared	0.958230	0.958230
Adj. R-Squared	0.957597	0.957557
MAPE	16.589589	16.589589

Importing necessary libraries and data¶

Data Overview¶

Observations¶

Observation¶

Observations¶

Summary of the Dataset¶

Observation¶

Observations¶

Observations¶

check for unique values in the column¶

Observations¶

Missing Values¶

Observations¶

Exploratory Data Analysis (EDA)¶

Lets explore numerical values¶

Observations on screen_size¶

Observations¶

Observations on main_camera_mp¶

Observations¶

Observations on selfie_camera_mp¶

Observations¶

Observations on int_memory¶

Observations¶

Observations on ram¶

Observations:¶

Observations on Battery¶

Observations:¶

Observations on weight¶

Observations¶

Observations on release_year¶

Observations.¶

Observations on days_used¶

Observations¶

Observations on new_price¶

Observations.¶

Observations on used_price¶

Observations¶

Let us explore categorical variables¶

Observations on OS¶

Observations¶

Observations on 4g¶

Observations¶

Observations on 5g¶

Observation¶

Bivariate Analysis¶

Observations¶

Bivariate Scatter Plots¶

Observations¶

Relationship between release_year and used_price¶

Observation¶

Relationship between used_price and days_used¶

Observations¶

Relationship between used_price and new_price¶

Observations¶

Relationship between used_price and ram¶

Observations¶

Relationship between used_price and int_memory¶

Observations¶

Relationship between used_price and weight¶

Observations¶

Relationship between used_price and battery¶

Observations¶

Relationship between used_price and main_camera_mp¶

Observations¶

Relationship between used_price and selfie_camera_mp¶

Observation¶

Relationship between used_price and screen_size¶

Observations¶

Check os by brand_name¶

Observations¶

check os by 4g¶

Observations¶

Check os by 5g¶

Observations¶

check 5g on brand_name¶

Observations¶

Check 4g on 5g¶

Observations¶

Used_price vs os¶

Observations¶